In the given diagram, we want to identify the transformation that maps △PQM onto △KJN.
We cannot map △PQM onto △KJN by moving △PQM and maintaining its orientation, so it is not a translation. The transformation is not a reflection because there is no line of symmetry between △PQM and △KJN. Also, we can see that △KJN is not a rotation of △PQM. The mapping looks like a glide reflection.
Writing the Rule
A glide reflection is the composition of a translation and a reflection across a parallel line to the direction of translation. Let's perform a glide reflection on △PQM and see if we can map it onto △KJN.
We can see that the glide reflection that maps △PQM onto △KJN consists of a translation 4 units to up, followed by a reflection across the line x=4. This composition of transformations can be written as (T_(<0,4>) ∘ R_(x=4))(x,y).
